Univariate Akima interpolation
The function returns a list of points which smoothly interpolate given data points, similar to a curve drawn by hand.
aspline(x, y=NULL, xout, n = 50, ties = mean, method="original", degree=3)
x, y |
vectors giving the coordinates of the points to be
interpolated. Alternatively a single plotting structure can be
specified: see |
xout |
an optional set of values specifying where interpolation is to take place. |
n |
If |
ties |
Handling of tied |
method |
either |
degree |
if improved algorithm is selected: degree of the polynomials for the interpolating function |
The original algorithm is based on a piecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive interval of the given points. In this method, the slope of the curve is determined at each given point locally, and each polynomial representing a portion of the curve between a pair of given points is determined by the coordinates of and the slopes at the points.
A list with components x and y,
containing n coordinates which interpolate the given data
points.
Akima, H. (1970) A new method of interpolation and smooth curve fitting based on local procedures, J. ACM 17(4), 589-602
Akima, H. (1991) A Method of Univariate Interpolation that Has the Accuracy of a Third-degree Polynomial. ACM Transactions on Mathematical Software, 17(3), 341-366.
## regular spaced data x <- 1:10 y <- c(rnorm(5), c(1,1,1,1,3)) xnew <- seq(-1, 11, 0.1) plot(x, y, ylim=c(-3, 3), xlim=range(xnew)) lines(spline(x, y, xmin=min(xnew), xmax=max(xnew), n=200), col="blue") lines(aspline(x, y, xnew), col="red") lines(aspline(x, y, xnew, method="improved"), col="black", lty="dotted") lines(aspline(x, y, xnew, method="improved", degree=10), col="green", lty="dashed") ## irregular spaced data x <- sort(runif(10, max=10)) y <- c(rnorm(5), c(1,1,1,1,3)) xnew <- seq(-1, 11, 0.1) plot(x, y, ylim=c(-3, 3), xlim=range(xnew)) lines(spline(x, y, xmin=min(xnew), xmax=max(xnew), n=200), col="blue") lines(aspline(x, y, xnew), col="red") lines(aspline(x, y, xnew, method="improved"), col="black", lty="dotted") lines(aspline(x, y, xnew, method="improved", degree=10), col="green", lty="dashed") ## an example of Akima, 1991 x <- c(-3, -2, -1, 0, 1, 2, 2.5, 3) y <- c( 0, 0, 0, 0, -1, -1, 0, 2) plot(x, y, ylim=c(-3, 3)) lines(spline(x, y, n=200), col="blue") lines(aspline(x, y, n=200), col="red") lines(aspline(x, y, n=200, method="improved"), col="black", lty="dotted") lines(aspline(x, y, n=200, method="improved", degree=10), col="green", lty="dashed")
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